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REPORTFORLAB A10: MECHANICAL OSCILLATIONS

Nathaniel Kan11/14/01

ABSTRACT:

In this lab we studied the relationship the harmonic motion of a spring-mass system when

energy is conserved, when the system is damped and when a sinusoidal force drives thedamped system. We then compared the actual results with the theoretical values.

PURPOSE:

See A10 Instruction Sheet page 1.

PRINCIPLES:

The main principle is Equation (6) on A9 Instruction Sheet page 4:

V2 = -N2(dPhi/dt) = -N1N2(mu0 R2 A / 2(R2 + X2)) (cos Theta) (di/dt)

This states that the induced voltage in a second coil will be proportional to the currentrunning through the first coil causing the electromagnetic field.

PROCEDURE:

We start by connecting the circuit in the following manner. We connect the larger 400-

turn coil to the function generator, through the resistor built into its base. We set thefrequency of the function generator to 2000 Hz and turn the amplitude to maximum. Weset the function to triangle wave. The coil is then connected to Channel 1 of an

oscilloscope. We then take the slope of the triangle wave from the oscilloscope.

Next the smaller detector coil is connected directly to Channel 2 of the oscilloscope. We

set the oscilloscope to display both channels simultaneously. Then we observe the shape

of each wave, the amplitude, and the frequency. We change the frequency of the function

generator to 4000 Hz, keeping the amplitude the same, and repeat the measurements. Wethen change the function generated to a sine wave, and repeat measurements at 2000 Hz

and 4000 Hz.

DATA:

See Lab book page 36 for the slope of the triangle wave.

See Lab book page 36 for a table of the results.

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RESULTS:

From our observations, we can tell that the signal observed on Channel 2 is theproportional to the derivative of the current through the first coil. We can see that when

the input signal on the first coil is a triangle wave, the signal on Channel 2 is a square

wave. During times when the slope is positive of the triangle wave on Channel 1, thesquare wave has a constant positive value. During times when the slope is negative of the

triangle wave, the square wave has a constant negative value.

When the function generated is a sine wave, the signal on Channel 2 is a cosine function,

simply proportional to the derivative of the sine wave.

When frequency of the input is increased, this means that the function reaches its wave

crest at a faster speed, meaning that the slope of the function is greater. This means thatthe amplitude of the signal on Channel 2 is increased, because that function is

proportional to the derivative of the input. When the generated function is a sine wave,

the cosine wave is phase shifted 90 degrees, because the derivative of a sine wave is acosine wave, which is a sine wave shifted 90 degrees.

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